Vol. 46 No. 2
SCIENCE IN CHINA (Series E)
April 2003
Theoretical and experimental study on surface tension and
dynamic surface tension of aqueous lithium bromide and
water with additive
CHENG Wenlong ()1, CHEN Zeshao ()1,
AKISAWA Atsushi ()2, HU Peng (
༑)1
& KASHIWAGI Takao ()2
1. University of Science & Technology of China, Hefei 230026, China;
2. Tokyo University of Agriculture & Technology, Tokyo 184-8588, Japan
Correspondence should be addressed to Cheng Wenlong (email: [email protected])
Received July 5, 2002
Abstract The surface tensions of water and aqueous lithium bromide (LiBr) with 2-ethyl-1-hexanol (2EH) and 1-octanol were measured using Wilhelmy plate method, and the oscillation of surface tension under the open condition for LiBr solution was observed. The dynamic surface
tensions of water and LiBr solution in the presence of the 2EH and 1-octanol vapor were measured
in this paper. The results showed that the additives vapor could obviously affect surface tension.
For water, the dynamic surface tension was also affected by the mass of the tested liquid; however,
for LiBr solution, the dynamic surface tension was not related to the mass of the tested solution.
According to the experimental results, the hypothesis that surface tension varies linearly with the
surface excess concentration is advanced, which could overcome the limit of Gibbs equation. The
equations of surface absorption and desorption are modified, the units of the adsorption coefficient
and desorption coefficient are unified; the effects of the liquid and vapor of additive on the surface
tension are unified; the theoretical relations of the static surface tension and dynamic surface tension with the relative contents of the liquid and vapor of additive are obtained under the combined
actions of them; the theoretical equations are validated by the experiments results.
Keywords: aqueous lithium bromide, surface tension, dynamic surface tension, additive, dynamic adsorption.
Heat and mass transfer of LiBr absorption chiller can be enhanced significantly through addition of trace amounts of additives, such as 2-ethyl-1-hexanol (2EH) and 1-octanol. This enhancement is apparently due to the interfacial convection, i.e. Marangoni convection. However, the
formation mechanism of Marangoni convection is still not clear[1].
Accurate static and dynamic surface tension data are necessary for studying the formation
mechanism of Marangoni convection. Unfortunately, the experimental data published are far from
sufficient, some even inconsistent[2
ü4]
. Recently, some research results show that the formation of
Marangoni convection may probably have close relation with the additive vapor[5,6]. However, it is
only recently that people started the research on the dynamic surface tensions[7,8] and on the effects of the additive vapor on the surface tensions[5,6]. And no the experimental data about the effect of the additive vapor on the dynamic surface tensions are available in literature. Therefore,
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SCIENCE IN CHINA (Series E)
Vol. 46
theoretical and experimental studies on surface tension and dynamic surface tension of aqueous
lithium bromide with additive may help reveal the formation mechanism of Marangoni convection
and enhance heat and mass transfer of LiBr absorption chiller.
In this work, the surface tension of water and LiBr solution with 2EH and 1-octanol under
closed condition and open condition, and the dynamic surface tensions of water and aqueous lithium bromide in the presence of 2EH and 1-octanol vapor were measured by Wilhelmy plate
method. The effects of additive (including liquid and vapor) on static and dynamic surface tension
of water and LiBr solution are analyzed.
1
Experiment on the effect of additive on surface tension
1.1
Experimental apparatus
Wilhelmy plate method is chosen for the measurements of static and dynamic surface tensions of water and LiBr solution with additive 2EH and 1-octanol. Surface tension is determined
by the force balance among the surface tension, gravity and pulling force to a thin platinum plate
which contacted and dipped into the tested liquid. Before each experiment, the platinum plate was
cleaned at a high temperature about 700k using an alcohol lamp to remove the impurities on the
plate.
In order to check the accuracy of the apparatus, some liquids were measured first. For distilled water and 2EH, the measured surface tensions were 72.49 and 26.64 mN/m at 21k, close to
the reference values of water 72.44 and 26.1 mN/m presented by Kulankara[5] and Kim[3] respectively.
1.2 Experiments in closed system and open system
The surface tensions of water and LiBr solution with different concentration of additive 2EH
and 1-octanol were measured. The distilled water used in this experiment was made by ourselves,
and all other chemical medicines were provided by Wako Pure Chemical Industries, LTD (Japan).
The LiBr concentration of the solutions was 55%, which was made of pure LiBr.H2O crystal and
distilled water. To control the concentration of additive with high accuracy, the additive was added
by a digital micropipet into solution, and then the solution was sealed into a tube. After having
been shaken vigorously, the tube was left at room temperature for 24 h. All samples were measured in a glass vessel with a diameter of 56.01 mm and a height of 58.91 mm, and at room temperature of about 23k. In order to evaluate the effect of volatilized additive on the vapor, every
sample was measured in a closed system (the sample is covered by a lid) and an open system (the
sample is exposed to air).
The measurement surface tensions of distilled water with 2EH and 1-octanol are listed in tables 1 and 2 respectively, and shown in fig. 1. The measurement stable surface tensions of 55%
LiBr solutions with these additives are listed in tables 3 and 4 respectively, and shown in fig. 2. In
the open system, the measurement surface tensions are oscillatory. Two typical oscillatory curves
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INFLUENCE OF ADDITIVES ON SURFACE TENSION
193
are shown in fig.3.
Table 1 Surface tension of water with 2EH
10
20
30
41.08
60
79.93
σ/mNm−1
C/ppm
72.53
5
71.97
70.07
68.04
66.02
63.55
60.75
59.84
56.14
σ*/mNm−1
72.58
72.13
70.63
69.60
67.46
64.68
61.88
60.63
57.12
C/ppm
200
σ/mNm−1
σ*/mNm−1
250
300
400
500
600
100
800
1000
150
1200
53.08
49.92
48.13
46.14
44.01
42.30
37.68
37.78
37.86
53.70
50.97
49.85
47.05
45.53
43.63
39.95
38.15
38.14
σ, Surface tension in a closed system; σ *, surface tension in an open system.
Table 2 Surface tensions of water with 1-octanol
C/ppm
5.35
10
20
35
50
75
σ/mNm−1
σ*/mNm−1
72.56
71.50
63.10
62.18
59.92
56.70
53.08
48.40
72.78
72.18
64.82
63.43
62.10
59.00
55.16
49.80
C/ppm
200
250
400
500
600
800
100
1000
149.83
1200
σ/mNm−1
44.48
41.23
32.82
30.30
29.75
29.99
29.24
29.57
σ*/mNm−1
45.58
42.84
35.48
32.20
32.62
30.69
30.98
30.79
1.3
Analysis
From the results and phenomena of these
experiments, we can conclude:
(1) The surface tensions of water and
LiBr solution can be affected by the concentration of additive. The surface tensions of
both water and LiBr solution decrease with an
increase in additive concentration, and tend to
steady when the concentration of additive is
increased to a certain value.
(2) The effect degree of additive concen- Fig. 1. Surface tension of H2O with Additive at 23. ,
tration on LiBr solution is lager than that on water + 2EH (closed); , water+2EH (open), +, water + 2EH
(Kulankara); , water+1-ictanol (close); , water+1-Oc- tanol
water. When surface tension becomes steady,
(open); , water+2EH (theoretical); ----, water+1-octanol
the additive concentration for LiBr solution is (theoretical).
lower than that for water.
(3) The surface tension in the open system is larger than that in the closed system. For LiBr
solution, this phenomenon is more obvious and its surface tension is unsteady.
Table 3 Surface tensions of 55% LiBr solution with 2EH
C/ppm
2.04
σ/mNm−1
76.42
C/ppm
100
−1
σ/mNm
35.75
5
74.82
200
34.28
10
20.7
40
60
80
65.77
55.56
51.35
41.98
40.53
400
35.58
600
34.97
800
34.88
1000
34.10
2000
34.87
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SCIENCE IN CHINA (Series E)
Vol. 46
C/ppm
σ/mNm−1
2
80.70
Table 4 Surface tensions of 55% LiBr solution with 1-octanol
5
10
20
30
40
50
80.97
71.60
59.62
52.92
45.84
40.68
C/ppm
80
37.32
90
34.03
σ/mNm−1
100
30.68
200
25.38
Fig. 2. Surface tension of 55% LiBr with additive at 23.
400
24.82
Fig. 3.
(open).
600
25.19
800
24.87
60
39.57
70
36.88
1000
24.70
The oscillation of surface tension of LiBr solution
From (1) we know that additive concentration in surface layer is higher than that in main
body and saturated earlier. Conclusion (2) shows that the effect of additive on solution is related to
the relative concentration of additive, because the solubility of additive in LiBr solution is only
about one tenth that in water. Conclusion (3) shows that the vapor concentration or partial pressure
of additive affects surface tension obviously, because the partial pressure of water in LiBr solution
is much lower than that in pure water, which raises the partial pressure of additive in LiBr solution;
thus when LiBr solution is exposed to air, the additive in surface layer volatilizes rapidly, and the
amount of the additive diffused from solution body to surface layer is less than that of volatilized
additive, and meanwhile LiBr solution can absorb moisture in air; therefore the additive concentration in surface layer deceases rapidly and surface tension rises rapidly. When the amount of the
additive diffused from solution body to surface layer is not equal to the amount of additive volatilized, surface tension would be unsteady.
2
The relation between surface tension and concentration of additive
2.1 Surface excess concentrationΓ.
When additive is added to a liquid system with free surface, the additive can exist in three
different states: (i) the additive dissolves in the liquid, (ii) the additive is adsorbed into the surface
layer, (iii) the additive volatilizes in vapor state in the vicinity of the interface. The amount of surfactant dissolved in the liquid is expressed as bulk concentration C (mol/m3), and the amount of
surfactant volatilized in vapor is expressed as partial pressure of additive vapor (or concentration
of additive in vapor) P/Pa. The concentration of additive adsorbed in the interface is termed “sur-
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INFLUENCE OF ADDITIVES ON SURFACE TENSION
195
face excess concentration Γ [kg/m2]” that is defined as the amount of surfactant adsorbed on a unit
area of the surface of the liquid.
2.2 Theoretical relation between surface tension and concentration of additive
For an ideal solution, the relation between surface tension and bulk concentration and surface
excess concentration is expressed by Gibbs equation as Γ = −
c dσ
⋅
. However, the limitations
RT dc
of Gibbs equation are: (i) it is difficult to simultaneously express both effects of liquid and vapor
of additive; (ii) the surface tension decreases with an increase in additive concentration to a steady
value, i.e. dσ dc = 0, but according to Gibbs equation, Γ should be 0 at this time; this is inconsis-
tent with the practice.
According to the experimental results and analysis, surface tension σof a solution with additive is directly controlled by the surface excess concentration Γwhich is affected not only by
additive liquid dissolved in bulk solution but also additive vapor existing on the gas side of the
interface. The minimum surface tension is defined as the critical surface tension σ c(mN/m), and
the saturated surface excess concentration is defined as the critical surface excess concentration Γc.
In this paper, the surface tension is assumed to vary linearly with the surface excess concentration
at the interface, i.e. the difference in surface tension σ with additive and surface tension without
additive σ 0 has a linear relationship with relative surface excess concentration φ Γ ,
(σ 0 − σ ) = φΓ (σ 0 − σ c )
where
or σ = σ 0 − φΓ (σ 0 − σ c ) = φΓσ c + (1 − φΓ )σ 0 ,
(1)
φ Γ is the relative surface excess concentration and defined as φΓ = Γ / Γc , and σ 0 is the
surface tension of solution without additive, mN/m.
2.3 Static surface tension σ e
There are two movement styles of additive on the surface layer. One is adsorption process:
the molecules of additive in the vicinity of interface are adsorbed to the interface, thus increasing
the surface excess concentration. The other is desorption process: the molecules of additive at the
interface are desorbed to the liquid side and vapor side near the interface, thus decreasing the surface excess concentration.
For the adsorption process, solution and gas are source of additive, and surface layer is sink.
According to the molecular kinetic theory and liner hypothesis, the adsorption rates from the liquid side and the vapor side can be expressed as
∂φΓ
∂t
∂φΓ
∂t
la =
kla X l ⋅ (1 − φΓ ), (2) ga =
kga X g ⋅ (1 − φΓ ), (3)
where Xl and Xg are the relative mass concentration of additive in the bulk solution and that on the
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SCIENCE IN CHINA (Series E)
Vol. 46
gas side, respectively. The factors kla and kga are defined as the liquid kinetic adsorption coefficient
and vapor kinetic adsorption coefficient, respectively, both in unit 1/s.
Desorption process is reverse to adsorption process, solution and gas are sink of additive, and
surface layer is source. Therefore, the desorption rates on the sides of liquid and vapor are in proportion to
φ Γ · (1Xl) and φ Γ · (1Xg) respectively. Considering Xl <<1, Xg<<1, they can be
written simply as
∂φΓ
∂t
∂φΓ
∂t
ld
= − kldφΓ ,
(4)
gd
= − kgdφΓ ,
(5)
where kld and kgd are proportionality factors defined as the liquid kinetic desorption coefficient and
the vapor kinetic desorption coefficient, respectively, in unit 1/s.
In Langmuir equation[10], the adsorption rates of surface is equal to K1P(1θ), and the desorption rate from the surface is equal to K1θ, where θ is the fraction of the surface covered, like
relative surface excess concentration φΓ in this paper. Langmuir equation can accord with the experimental results under limited condition. But the units of its coefficients K1 and K−1 are inconsistent, and the reason why the effect of gas additive is constant in desorption rate equation is not
clear. In some papers[8,9], the adsorption rates of surface is equal to klaC ( Γ c − Γ), where C is bulk
concentration; its unit is mol/m3, and the desorption rate from the surface is equal to kgd Γ, the
units of the coefficients are inconsistent, and their physical significances are not clear. From conclusion (2), it is more reasonable to use relative mass concentration of additives Xl and Xg and
relative surface excess concentration to express the effect of additive concentration on surface
tension. That can not only explain the difference in expressions between eqs. (2), (3) and eqs. (4),
(5), but also unify the units of kla, kga, kgd and kgd. Because eqs. (4) and (5) have the same function
format, the desorption effects of both liquid and vapor of additive can be expressed as
∂φΓ
∂t
d
= − kdφΓ ,
(6)
where the proportionality factor kd = kld + kgd , defined as the overall kinetic desorption coefficient, reflects the overall effects caused by desorption of additive from the interface to both sides
of liquid and gas. According to the former equations, the relation of surface excess concentration
and time can be expressed as
dφΓ ∂φΓ
=
dt
∂t
la
+
∂φΓ
∂t
ga
+
∂φΓ
∂t
d.
(7)
When the interface is in steady state, the adsorption process and desorption process reach
equilibriun, and both sides of eq. (7) are equal to zero. Substituting eqs. (2), (3) and (6) into eq.
(7), we obtain the relation of relative surface excess concentration and the amount of additive in
No. 2
INFLUENCE OF ADDITIVES ON SURFACE TENSION
197
the vicinity of the interface including liquid side
φΓ e =
aX l + bX g
1 + (aX l + bX g )
,
(8)
where φΓe is the relative surface excess concentration in equilibrium state, a = kla kd is equilibrium coefficient for liquid, and b = kga kd is equilibrium coefficient for gas. The coefficients a
and b express the potential ability of surface tropism and approach to constants for an isothermal
system and are independent of the surface excess concentration Γ [8]. Their values can be calculated by Xl, Xg and σ e. Substituting eq. (8) into eq. (1), the static surface tension in equilibrium can
be obtained
σe =
1
1 + aX l + bX g
σ0 +
aX l + bX g
1 + aX l + bX g
σc,
(9)
where σ e is the surface tension of solution with additive in the equilibrium, termed as static surface tension, mN/m.
3
Experimental verification for static surface tension equation
3.1 Effects of liquid additive on surface tensions
In the case where the additive is added in the solution directly in a closed system, although
the desorption of additive at the vapor-liquid interface to the vapor side can influence the performance of surface tension of the solution, the amount of additive on the vapor side is very small,
and the absorption of additive from vapor can be ignored compared to the absorption of liquid
additives. Therefore, eq. (9) can be simplified into
σe =
aX l
1
σ0 +
σc.
1 + aX l
1 + aX l
(10)
Eq. (14) is compared with the experimental
results of this work (figs. 1 and 2) as well as
with the other experimental results measured
by different methods (figs. 3 and 4). The
other parameters used in eq. (10) and the fitted equilibrium coefficient a are listed in table 5.
Figs. 4 and 5 show that the curves calculated by eq. (10) agree well with the experimental results on water and 55% LiBr
solution. In figs. 4 5, the data of Kim et al.[3]
measured by a Du Nouy ring method are obviously higher than others, because the sam-
Fig. 4.
Surface tension of LiBr with additives at 25. ,
LiBr(50%)+2EH 25k[2]; , LiBr(50%)+2EH 24k (Kim), ,
LiBr(50%)+1-Octanol 25k (Yao); , LiBr(50%)+1-octanol
22k (Ishida); , LiBr(50%)+2EH (theoretical); ---, LiBr
(50%)+1-octanol (theoretical).
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SCIENCE IN CHINA (Series E)
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Table 5 Parameters of static surface tensions of LiBr with additive
State
Solution
Additive
T
σ0
σc
a
Liquid
Water
2EH
23
72.4
36.0
6.2 × 103
1-Octanol
23
72.4
26.0
8.2 × 103
LiBr (55%)
2EH
23
90.2
34.0
8.3 × 104
1-octanol
23
90.2
24.0
5.4 × 104
LiBr (50%)
2EH
25
87.7
34.5
1.3 × 105
1-octanol
25
87.7
24.5
1.2 × 105
LiBr (50%)
2EH
50
84.8
34.0
2.9 × 104
1-octanol
50
84.8
25.0
5.5 × 104
Vapor
LiBr (60%)
2EH
25
95.6
34.0
b=2.1 × 104
For liquid additive the coefficient is a in eq. (10), and for vapor additive, the coefficient is b in eq. (11).
ple vessel was exposed to air for about 30 s to
measure a surface tension. Therefore the
volatilization of additive in the Gibbs surface
causes a decrease in the surface excess concentration, and which will result in a larger
measured surface tension than that in the
equilibrium case. The data of Yao et al.[2]
were measured by a drop volume method,
although the liquid drops with additive were
exposed to air too, an appropriate drop frequency can ensure that the time (about 1 s) of Fig. 5. Surface tension of LiBr with additives at 50. , LiBr
liquid drop exposed to air is much shorter (50%)+2EH 50k (Yao); , LiBr(50%)+2EH 48k (Kim), ,
than that by the Du Nouy ring method. Thus, LiBr(50%)+1-octanol 50k (Yao); , LiBr(50%)+2EH (theothe values obtained by Yao et al. are smaller retical); ---, LiBr(50%)+1-octanol (theoretical)
than that by Kim. The values obtained by Ishida et al.[4] were measured by a laser-beam reflection
method, and the sample could be measured in the equilibrium state in a closed system. Therefore,
Ishida’s values are the smallest. The parameters in eq. (1) are fitted by the data of Yao et al.[2],
which are in general considered to be more accurate. For water, the critical surface tensions
σ c are not experimental values like that for LiBr solution, but the results fitted by experimental
data are a little lower than experimental data, which are 37.5 and 29.5 mN/m for 2EH and
1-octanol, respectively. The possible reason for this difference is that the measurements perhaps
have a little system deviation or probably the micelle is generated at the interface when surface
excess concentration approaches to the critical value.
3.2 Effects of vapor additives on surface tensions
Herold[6] considered that the effect of vapor additives was deterministic for surface tension,
and the effect in turn caused the Marangoni convection at last. However, it is a bias to overemphasize vapor side additive, because surface tension can be affected by liquid additive as well as vapor additive through surface layer. Vapor additive agitates Marangoni convection by impressing
the interface. In this case, when the LiBr solution drop is surrounded by vapor additive, the
No. 2
INFLUENCE OF ADDITIVES ON SURFACE TENSION
199
amount of additive in the bulk drop delivered
from the vapor side is very small, and the
adsorption of additive on the liquid side to
the interface can be ignored. Therefore, eq. (9)
can be expressed as
σe =
bX g
1
σ0 +
σ c.
1 + bX g
1 + bX g
(11)
The experimental values and the theory
curves are shown in fig. 6. The comparison
shows that theoretical equation (11) accords
with the experimental values very well. The Fig. 6. Surface tension of LiBr with 2EH vapor. , LiBr (60%)
experimental conditions and the parameters +2EH 25 (Yuan et al.); , LiBr(60%)+2EH 25 (theoretical).
in eq. (11) are listed in table 5. It can be
found that the magnitudes of coefficient a in eq. (10) and coefficient b in eq. (11) are similar, implying that the vapor additive of 2EH and 1-octanol may possibly cause Marangoni convection in
LiBr solution just like liquid additive of 2EH and 1-octanol.
4 Dynamic surface tension σ t
4.1 Theoretical equation of dynamic surface tension σ t
When the interface is in non-equilibrium state, or a fresh interface is forming, the surface
excess concentration changes with time (surface age) because of the adsorption process, and the
surface tension changes with time also. In this case, the surface tension changing with time is
termed dynamic surface tension σ t . A research of dynamic surface tension helps us to understand
Marangoni convection.
In the non-equilibrium case, substituting eqs.(2), (3) and (6) into eq.(7), we have
dφΓ
= (kla X l + k ga X g + kd )(φΓ e − φΓ ),
dt
(12)
where the dynamic adsorption parameter k is defined as k = kla X l + k ga X g + kd . k is a function
of concentration of additive in solution and gas. However, the effect of the additive variation in
solution and gas on additive concentration can be ignored in dynamic absorption process; therefore k is assumed to be a constant. On this assumption, eq. (10) is integrated from the initial condition, t = 0, Γ = 0, and the function of surface excess concentration can be obtained
φΓt = φΓ e (1 − e− kt ),
where
(13)
φ Γt is the dynamic relative surface excess concentration. Substituting eq. (11) into eq. (1),
we have σ t = σ 0 − (σ 0 − σ e )(1 − e− kt ).
(14)
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SCIENCE IN CHINA (Series E)
Vol. 46
However, eq. (12) is very sensitive to time.
In order to improve the accuracy of eq. (12),
an exponent n is introduced. Therefore, eq.
(12) is replaced by σ t = σ 0 − (σ 0 − σ e )[1 − e− ( kt ) ].
n
(13)
The exponent n approximates to a constant,
and n ≈ 0.5 in all cases. The value of k is the
fitted result using experimental data.
4.2 Effects of liquid additives on dynamic
surface tensions
Fig. 7. Dynamic surface tension of LiBr with additives. ,
Kim[7] et al. measured the dynamic surLiBr (53%) +1-octanol (ref. [8]); , LiBr(53%)+2EH(ref. [8]);
, LiBr(50%)+2EH (ref. [9]); , LiBr(40%)+2EH (ref. [9]); , face tensions of different concentration of
LiBr(30%)+2EH (ref. [9]).
LiBr solution solutions at 30%, 40% and
50% with 500 ppm 2EH by a modified maximum bubble pressure method. But they did not give
the static surface tension of those solutions with 500 ppm 2EH. Kren[8] measured the dynamic
surface tensions of 53% LiBr solution with 76.1ppm 2EH and 22.8 ppm 1-octanol by a bubble
pressure tensiometer. The static surface tensions of these two solutions are 38 and 43
mN/m, respectively. Some experimental results show that the static surface tensions of
different LiBr solutions with 2EH higher than
100 ppm approach to a constant about 34
mN/m. This constant 34 mN/m is chosen as
static surface tension to fit the experimental
results provided by Kim[7]. The experimental
dynamic surface tensions and the theoretical
curves fitted by eq. (13) (n = 0.5) are shown
in fig. 10, and the experimental conditions
and parameters in eq. (13) are listed in table 6. Fig. 8. DST of H2O with 1-octanol vapor. , Water+1-ocIt is obvious that the theoretical curves can fit tanol (m = 31.28 g); , water+1-octanol (m = 7.72 g); , theoretical curve (m = 31.28 g); ----, theoretical curve (m = 7.72 g).
the experimental results with high accuracy.
4.3 Dynamic surface tension of water and LiBr solution with additive vapor
The dynamic surface tension of water and LiBr solution with additive has scarcely been
studied, especially for the dynamic surface tension of liquid in the presence of vapor of additive.
The dynamic surface tension is believed to be a possible essential cause leading to Marangoni
convection. Therefore, it is necessary to obtain experimental data of dynamic surface tension of
aqueous with additive vapor.
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INFLUENCE OF ADDITIVES ON SURFACE TENSION
201
The dynamic surface tensions (DST) of water and LiBr solution with additive vapor of 2EH
and 1-octanol were measured by Wihelmy plate method for the first time (figs. 8 and 9). The concentration of LiBr solution was 53.9% (Honsou Chemical LTD, Japan). The other reagents and
water were the same as those used in the first experiment. A sample vessel 66.0 mm in diameter
and 14.0 mm in height filled with sample and additive, was left in the closed testing space at room
temperature for at least 24 h so that the testing space was filled by the vapor of additive in equilibrium state before experiment. During the experiment, the temperature was controlled at about 24
. To observe the effect of additive diffusion from surface to solution body on surface tension,
the experiments were done at lease twice with the same solution of different qualities. It should be
noted that the thin film of additive on the interface is so sensitive that a tiny disturbance to the
vessel may result in a larger oscillation of the measured surface tension. Therefore, any touch to
the experimental apparatus should be avoided.
Fig. 9. DST of H2O with 2EH vapor. , Water+2EH (m =
Fig. 10. DST of LiBr with 1-octanol vapor. , LiBr+1-oc-
39.34 g); , water + 2EH (m = 7.65 g); , theoretical
tanol (m = 65.91 g); +, LiBr+1-octanol (m = 14.23 g); ,
curve (m = 39.34 g); ----, theoretical curve (m = 7.65 g).
theoretical curve.
Table 6 The parmeters of dynamic surface tension of LiBr with additive
Co1%
Additive
Ca2/ppm
σ 0 /mNm−1
σ e /mNm−1
k /s−110−5
53
2EH
76.1
91.0
38.0
1.30
53
1-octanol
22.8
91.0
43.0
0.67
50
2EH
500
89.0
34.0
6.24
40
2EH
500
84.5
34.0
11.7
30
2EH
500
81.2
34.0
25.0
Co1, concentration of lithium bromide in the solution; Ca2, concentration of additive in the solution.
The dynamic surface tensions of water with 1-octanol vapor and 2EH vapor, LiBr solution
with 1-octanol vapor and 2EH vapor are shown in figs. 47, respectively. In order to identify the
difference in the experimental results and the theoretical results clearly, the horizontal axes (time)
in these figures are transferred to logarithm time. The experimental conditions and the parameters
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Vol. 46
in eq. (13) are listed in table 7.
Table 7 The parmeters of dynamic surface tension of LiBr solution with additive
Tested solution
M/g
H/mm
σ 0 /mNm−1
σe /mNm−1
k (s−1)10−6
Water+2EH
39.34
7.65
11.5
2.2
72.4
72.4
53.0
48.5
1.60
0. 96
Water+1-octanol
31.28
7.72
9.1
2.3
72.4
72.4
52.0
48.0
1.09
0. 96
60.35
11.0
89.0
40.0
3.48
LiBr+2EH
20.07
3.8
89.0
40.0
3.48
12.54
2.3
89.0
40.0
3.48
LiBr+1-octanol
65.91
14.23
12.0
2.6
89.0
89.0
32.0
32.0
6.24
6.24
M, mass of the tested sample; H, height of the vessel with sample.
It can be found that the dynamic surface
tensions decrease with time quickly at the beginning. However the decrease rates decrease
with time, and finally the surface tensions approach to a certain value. There is a large difference between the experimental results of
water and LiBr solution. For water with vapor
of 2EH and 1-octanol, the dynamic surface
tensions are related evidently to the mass of
solution sample filled in the sample vessel, and
the larger the mass of the solution, the greater
Fig. 11. DST of LiBr with 2EH vapor.
the surface tensions (fig. 11). For LiBr solution
with vapor of 2EH and 1-octanol, the performance of dynamic surface tensions is almost not affected by the mass of the tested sample.
It is found that the theoretical curves agree with the experimental results very well except for
the initial measured interval about 100200 s. This is due to the effect of the additives adsorbed
to the detecting platinum plate. In these experiments, it took 2030 s for the detecting platinum
plate to touch the solution surface after the experiment started. During this process, some additives
were adsorbed from the additive vapor in the closed testing place to the plate. After the plate
touches the surface, the additives adsorbed to the plate will diffuse to the vapor-liquid interface
near the plate, resulting in smaller surface tensions in the initial interval than the calculated. Because the effect of additive on the surface tensions of LiBr solution is much more sensitive than
that of water, the discrepancy between the experimental data and the theoretical results of LiBr
solution is much larger than that of water. Therefore, for LiBr solution, the additive adsorbed to
the plate is the dominant effect factor to the deviation in the initial interval; for water with additive,
the effect of the additive concentration is not as sensitive as that of LiBr solution. In these cases,
the disturbance of the interface caused by the touching plate will affect the surface tension greatly
in the initial interval. This phenomenon is related to the dynamic adsorption parameter k. k in eq.
(13) of solution with vapor additive is much smaller than that of solution with liquid additive (tables 6 and 7). This is possibly because the concentration of vapor additive is too low in the present
No. 2
INFLUENCE OF ADDITIVES ON SURFACE TENSION
203
experiments.
5
Conclusion
The surface tensions of distilled water and 55% LiBr solutions with 2EH and 1-octanol were
measured by Wilhelmy plate method in a closed system and an open system. The dynamic surface
tensions of water and LiBr solution (53.9%) with 1-octanol and 2EH were measured by the Wilhelmy plate method for the first time. The equations of static and dynamic surface tension of solution with liquid additive or/and vapor additive were obtained and validated by the experiments.
The conclusions of this work are
1) The additive in solution or in gas can cause the surface tension of solution descending; the
effect of these two state is similar.
2) The concentration of additive can affect the surface tension of solution. The surface tensions of both water and LiBr solution decrease with an increase in additive concentration, and tend
to steady when the concentration of additive is increased to a certain value.
3) The surface tension of solution with additive is directly controlled by the surface excess
concentration Γ.
4) It is reasonable to use relative mass concentration of additive and relative surface excess
concentration to express the effect of additive concentration on surface tension.
5) Any factors that change the surface excess concentration of additive will change the surface tension. For example, the surface tension in an open system is bigger than that in a closed
system under the same condition, and this phenomenon is more obvious for LiBr solution.
Acknowledgements This project is supported by the Special Foundation of Engineering Science School of USTC and
the National Natural Science Foundation of China (Grant No. 50206020).
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